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(2003 / vol.6 / no.2)
Aluthge Transforms of Operators
Il Bong Jung
Pages. 59-68     



The Aluthge transform $widetilde{T}$ (defined below) of an
operator $T$ on
Hilbert space has been studied extensively, most often in connection with $p$%
-hyponormal operators. In cite{JKP1} one initiated a study of
various relations between an arbitrary operator $T$ and its
associated $widetilde{T} $, and this study was continued to the
theories of spectral pictures, Aluthge and Duggal iterations, and
numerical ranges. In this article we survey those recent works and
give some related open problems.



1. Introduction
2. Spectral theory
3. Spectral pictures
4. Some transforms
5. Aluthge iterates
6. Backward Aluthge iterates
7. Invariant subspace problem



Aluthge transforms, Duggal transforms, $p$-hyponormal operators, spectrum, spectral pictures, completely contractive maps



47A15, 47B20, 47A10, 47A12, 47